Which of the following may represent the curve x = 2y+ 3?

Options

A.
B.
C.
D.

Answer

To solve the question "Which of the following may represent the curve x = 2y + 3?", we will follow these steps:

### Step 1: Rearranging the Equation
We start with the given equation:
\[ x = 2y + 3 \]

We want to express this in the standard form of a linear equation, which is typically written as \( y = mx + c \). To do this, we will isolate \( y \).

### Step 2: Isolating \( y \)
Rearranging the equation:
\[ 2y = x - 3 \]
Now, divide both sides by 2:
\[ y = \frac{1}{2}x - \frac{3}{2} \]

### Step 3: Identifying the Slope and Intercept
From the equation \( y = \frac{1}{2}x - \frac{3}{2} \), we can identify:
- The slope \( m = \frac{1}{2} \)
- The y-intercept \( c = -\frac{3}{2} \)

### Step 4: Analyzing the Slope
Since the slope \( \frac{1}{2} \) is positive, this means that the line rises as it moves from left to right. The angle of the line with the x-axis will be between 0 degrees and 90 degrees.

### Step 5: Analyzing the Y-Intercept
The y-intercept \( -\frac{3}{2} \) indicates that the line crosses the y-axis below the origin (at -1.5 on the y-axis).

### Step 6: Evaluating Options
Now, we need to evaluate the given options (which are not provided in the question but are assumed to be graphical representations of lines):
- We will reject any options where the angle with the x-axis is greater than 90 degrees (i.e., lines that slope downwards).
- We will also reject any options where the y-intercept is positive (above the origin).

### Conclusion
After analyzing the options based on the slope and y-intercept, we will select the option that has:
1. A positive slope (rising line).
2. A negative y-intercept (crossing the y-axis below the origin).